Most Important Selected Qs for JEE AdvancedMathematicsIndefinite Integration

Let f(x)= x^ x (1+x x n x+ x) d x and f ( 2 )= ^2 4 , then the value of f(x) is

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aligned & f(x)= x^ x (1+x x x+ x) d x & Let f(x)=x^ x & 1 f(x) f^ (x)= x 1 x + x x (Taking log on both side and differentiating) & f^ (x)=f(x) [ x+x x x x ] & x f^ (x)=f(x) [ x+x x x f^ (x)=f(x)[ x+x x x] . & f(x)= [f(x)+f(x)(x x n x+ x)] d x & = [f(x)+x f^ (x) ] d x= d d x x f(x) =x f(x)+c & f(x)=x x^ x +c f ( 2 )= 2 ^ 2 +c= ^2 4 c=0 & f| f( ) |=f| ( )|=f(1)=1 aligned

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